Strange residues after separation of mesh
OK, I think you were in face selection mode, and you have unconnected edges. That is what you are seeing now. Because the edges were not part of a face they will stay unselected when using face select mode. 

PS You also have a LOT of duplicate vertices, 83,559 to be exact, Not related to this, but probably not going to help you.

To delete the unconnected edges, switch to edge select mode, and select one of the loose edges.
Then from the 3D view header Select > Select Similar > Amount of Faces Around an Edge, or just simply ShiftG then A. Now delete all the selected vertices with X > Vertices, or Delete > Vertices.